login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A328500 Number of inversion sequences of length n avoiding the consecutive pattern 102. 1
1, 1, 2, 6, 22, 96, 492, 2902, 19350, 143918, 1181540, 10614698, 103589738, 1091367634, 12346368424, 149276823258, 1921099070062, 26220186000950, 378308908684300, 5753387612678314, 91988260677198002, 1542570178562361018, 27072325866355742048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Juan S. Auli, Pattern Avoidance in Inversion Sequences, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.

Juan S. Auli, Sergi Elizalde, Consecutive Patterns in Inversion Sequences, arXiv:1904.02694 [math.CO], 2019. See Table 3.

FORMULA

a(n) ~ n! * c * d^n * n^alfa, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))), alfa = 0.294868853646259565..., c = 2.22826071050847602... - Vaclav Kotesovec, Oct 19 2019

MAPLE

b:= proc(n, j, t) option remember; `if`(n=0, 1, add(

`if`(i<=j or i>=t, b(n-1, i, j), 0), i=1..n))

end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..25); # Alois P. Heinz, Oct 18 2019

MATHEMATICA

b[n_, j_, t_] := b[n, j, t] = If[n == 0, 1, Sum[If[i <= j || i >= t, b[n - 1, i, j], 0], {i, 1, n}]];

a[n_] := b[n, 0, 0];

a /@ Range[0, 25] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A049774, A071075, A200404.

Sequence in context: A253948 A248836 A351919 * A180389 A177389 A130907

Adjacent sequences: A328497 A328498 A328499 * A328501 A328502 A328503

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec and Juan S. Auli, Oct 17 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 11:21 EST 2022. Contains 358700 sequences. (Running on oeis4.)